| Definitions | ||
| #1 | When three or more lines intersect at one point. | Concurrent |
| #2 | The point of concurrency for the perpendicular bisectors of a triangle. | Circumcenter |
| #3 | The point of concurrency for the angle bisectors. | Incenter |
| #4 | When all three points of a triangle lie on a circle and the circumcenter of the triangle is the center. | Circumscribed Triangle |
| #5 | The use of indirect reasoning, often where only one statement and its negation are the possible outcomes. | Indirect Proof |
| Theorems | ||
| #1 | Which theorem says that if two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle? | Hinge |
| #2 | The corollary to the Triangle Exterior Angle theorem says what about the following picture and its angles? | Angle 1's measure is greater than angle two and three. |
| #3 | The triangle inequality theorem says the sum of the lengths of any two sides of a triangle is _____________ than the length of the third side. | Greater than |
| #4 | If a point is on the perpendicular bisector of a segment, then it is _____________ from the endpoints of the segment. | Equidistant |
| #5 | The concurrency of medians theorem states that the point of concurrency is exactly __________ the distance from each vertex to the midpoint of the opposite side. | Two-Thirds (2/3) |
| Theorem Applications | ||
| #1 | What is always true about the altitudes of a triangle, other than that they make right angles? | They are concurrent |
| #2 | If triangle ABC has a bisector that runs from B to D, and D is the midpoint of AC, what does this mean for lengths AB and CB? | They are congruent |
| #3 | If a point is on the bisector of an angle, then the point is ___________ from the sides of the angles. | Equidistant |
| #4 | The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the _______________. | Vertices |
| #5 | The bisectors of the angles of a triangle are concurrent at a point equidistant from the ______________ of the triangle. | Sides |
| Miscellaneous | ||
| #1 | True or false: Medians make right angles with the lines they bisect. | False |
| #2 | What is the first step in writing an indirect proof? | Make a negation assumption |
| #3 | Which of these three statements negate each other: A is parallel to B, A is congruent to B, A is perpendicular to B. | First and Third |
| #4 | Write a negation to the following statement: We did not go to class. | We did go to class. |
| #5 | What type of triangle will have an orthocenter outside of the triangle? | Obtuse |
| More Definitions | ||
| #1 | A segment whose endpoints are a vertex and the midpoint of the opposite side. | Median |
| #2 | The perpendicular segment from a vertex of the triangle to the line containing the opposite side. | Altitude |
| #3 | The point of concurrency of the medians. | Centroid |
| #4 | The point of concurrency of the altitudes. | Orthocenter |
| #5 | When considering all possibilities and then determining all but one is false, and the remaining answer is true. | Indirect Reasoning |
| Final Question | |
| What type of triangle will have the orthocenter and centroid in the same position? | Equilateral |